Packages and Inputs

library(xgboost) # for xgboost
library(tidyverse) # general utility functions
diseaseInfo <- read_csv("C:/Users/User/Desktop/university/machine learning/machine learning - salini/dataset/Outbreak_240817.csv")
Parsed with column specification:
cols(
  .default = col_character(),
  Id = col_double(),
  latitude = col_double(),
  longitude = col_double(),
  sumAtRisk = col_double(),
  sumCases = col_double(),
  sumDeaths = col_double(),
  sumDestroyed = col_double(),
  sumSlaughtered = col_double(),
  humansAge = col_double(),
  humansAffected = col_double(),
  humansDeaths = col_double()
)
See spec(...) for full column specifications.

Preparing our data & selecting features

The core xgboost function requires data to be a matrix. A matrix is like a dataframe that only has numbers in it. A sparse matrix is a matrix that has a lot zeros in it. XGBoost has a built-in datatype, DMatrix, that is particularly good at storing and accessing sparse matrices efficiently.

head(diseaseInfo)

our data will need some cleaning before it’s ready to be put in a matrix. To prepare our data, we have a number of steps we need to complete:

Remove information about the target variable from the training data

diseaseInfo_humansRemoved <- diseaseInfo %>% select(-starts_with("human")) # get the subset of the dataframe that doesn't have labels about humans affected by the disease

Let’s create a new vector with the labels

diseaseLabels <- diseaseInfo %>% 
  select(humansAffected) %>% # get the column with the # of humans affected
  is.na() %>% # is it NA?
  magrittr::not() # switch TRUE and FALSE (using function from the magrittr package)

# check out the first few lines
head(diseaseLabels) # of our target variable
     humansAffected
[1,]          FALSE
[2,]          FALSE
[3,]          FALSE
[4,]          FALSE
[5,]          FALSE
[6,]          FALSE
head(diseaseInfo$humansAffected) # of the original column
[1] NA NA NA NA NA NA

Reduce the amount of redundant information

diseaseInfo_numeric <- diseaseInfo_humansRemoved %>%
    select(-Id) %>% # the case id shouldn't contain useful information
    select(-c(longitude, latitude)) %>% # location data is also in country data
    select_if(is.numeric) # select remaining numeric columns

# make sure that our dataframe is all numeric
str(diseaseInfo_numeric)
tibble [17,008 x 5] (S3: tbl_df/tbl/data.frame)
 $ sumAtRisk     : num [1:17008] 248000 122 1283 NA NA ...
 $ sumCases      : num [1:17008] 12 6 112 1 1 1 19 2 1600 5 ...
 $ sumDeaths     : num [1:17008] 12 1 0 1 1 1 19 2 0 5 ...
 $ sumDestroyed  : num [1:17008] 50000 0 NA 0 NA NA 0 0 4000 0 ...
 $ sumSlaughtered: num [1:17008] 0 0 7 0 NA NA 0 0 0 0 ...

Convert categorical information (like country) to a numeric format

head(diseaseInfo$country)
[1] "South Africa"       "Russian Federation" "Zimbabwe"           "South Africa"      
[5] "Czech Republic"     "Czech Republic"    
model.matrix(~country-1,head(diseaseInfo)) # one-hot matrix for just the first few rows of the "country" column
  countryCzech Republic countryRussian Federation countrySouth Africa countryZimbabwe
1                     0                         0                   1               0
2                     0                         1                   0               0
3                     0                         0                   0               1
4                     0                         0                   1               0
5                     1                         0                   0               0
6                     1                         0                   0               0
attr(,"assign")
[1] 1 1 1 1
attr(,"contrasts")
attr(,"contrasts")$country
[1] "contr.treatment"
region <- model.matrix(~country-1,diseaseInfo)

# check out the first few lines of the species
head(diseaseInfo$speciesDescription)
[1] "domestic, unspecified bird" "domestic, swine"            "domestic, cattle"          
[4] "wild, unspecified bird"     "wild, wild boar"            "wild, wild boar"           

diseaseInfo_numeric$is_domestic <- str_detect(diseaseInfo$speciesDescription, "domestic")
# grab the last word of each row and use that to create a one-hot matrix of different species

# get a list of all the species by getting the last
speciesList <- diseaseInfo$speciesDescription %>%
    str_replace("[[:punct:]]", "") %>% # remove punctuation (some rows have parentheses)
    str_extract("[a-z]*$") # extract the least word in each row

# convert our list into a dataframe...
speciesList <- tibble(species = speciesList)

# and convert to a matrix using 1 hot encoding
options(na.action='na.pass') # don't drop NA values!
species <- model.matrix(~species-1,speciesList)

# add our one-hot encoded variable and convert the dataframe into a matrix
diseaseInfo_numeric <- cbind(diseaseInfo_numeric, region, species)
diseaseInfo_matrix <- data.matrix(diseaseInfo_numeric)

Split the dataset to model

# get the numb 70/30 training test split
numberOfTrainingSamples <- round(length(diseaseLabels) * .7)

# training data
train_data <- diseaseInfo_matrix[1:numberOfTrainingSamples,]
train_labels <- diseaseLabels[1:numberOfTrainingSamples]

# testing data
test_data <- diseaseInfo_matrix[-(1:numberOfTrainingSamples),]
test_labels <- diseaseLabels[-(1:numberOfTrainingSamples)]
# put our testing & training data into two seperates Dmatrixs objects
dtrain <- xgb.DMatrix(data = train_data, label= train_labels)
dtest <- xgb.DMatrix(data = test_data, label= test_labels)

Analysis

Supervised Learning

set.seed(1234)
diseaseInfo <- diseaseInfo[sample(1:nrow(diseaseInfo)), ]
model <- xgboost(data = dtrain,  
                 nround = 2, # max number of boosting iterations
                 objective = "binary:logistic")  # objective function
[1] train-error:0.019654 
[2] train-error:0.019654 
# generate predictions for our held-out testing data
pred <- predict(model, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
[1] "test-error= 0.000980007840062721"

Tuning our Model

# train an xgboost model
model_tuned <- xgboost(data = dtrain,          
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 2, # max number of boosting iterations
                 objective = "binary:logistic") # objective function 
[1] train-error:0.019654 
[2] train-error:0.019654 
# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
[1] "test-error= 0.000980007840062721"

There are two things we can try to see if we improve our model performance: - Account for the fact that we have imbalanced classes - Train for more rounds

# get the number of negative & positive cases in our data
negative_cases <- sum(train_labels == FALSE)
postive_cases <- sum(train_labels == TRUE)

# train a model using our training data
model_tuned <- xgboost(data = dtrain,           
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 10, # number of boosting rounds
                 early_stopping_rounds = 3, # if we don't see an improvement in this many rounds, stop
                 objective = "binary:logistic", # objective function
                 scale_pos_weight = negative_cases/postive_cases) # control for imbalanced classes
[1] train-error:0.020410 
Will train until train_error hasn't improved in 3 rounds.

[2] train-error:0.020494 
[3] train-error:0.020494 
[4] train-error:0.020914 
Stopping. Best iteration:
[1] train-error:0.020410
# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
[1] "test-error= 0.00392003136025088"

… TODO

# train a model using our training data
model_tuned <- xgboost(data = dtrain,            
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 10, # number of boosting rounds
                 early_stopping_rounds = 3, # if we don't see an improvement in this many rounds, stop
                 objective = "binary:logistic", # objective function
                 scale_pos_weight = negative_cases/postive_cases, # control for imbalanced classes
                 gamma = 1) # add a regularization term
[1] train-error:0.020410 
Will train until train_error hasn't improved in 3 rounds.

[2] train-error:0.020494 
[3] train-error:0.020494 
[4] train-error:0.020914 
Stopping. Best iteration:
[1] train-error:0.020410
# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
[1] "test-error= 0.00392003136025088"

Interpretation

# plot them features! what's contributing most to our model?
xgb.plot.multi.trees(feature_names = names(diseaseInfo_matrix), 
                     model = model)
Column 2 ['No'] of item 2 is missing in item 1. Use fill=TRUE to fill with NA (NULL for list columns), or use.names=FALSE to ignore column names. use.names='check' (default from v1.12.2) emits this message and proceeds as if use.names=FALSE for  backwards compatibility. See news item 5 in v1.12.2 for options to control this message.
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

Because we’re using a logistic model here, it’s telling us the log-odds rather than the probability

# convert log odds to probability
odds_to_probs <- function(odds){
    return(exp(odds) / (1 + exp(odds)))
}

# probability of leaf above countryPortugul
odds_to_probs(-0.599)
[1] 0.3545725
# get information on how important each feature is
importance_matrix <- xgb.importance(names(diseaseInfo_matrix), model = model)

# and plot it!
xgb.plot.importance(importance_matrix)

Unsupervised Learning

# diseaseInfo_numeric.pca <- prcomp(diseaseInfo_numeric[, c(1:7,10,11)],
#                                   center = TRUE,
#                                   scale = TRUE)
diseaseInfo_numeric
---
title: "R Notebook"
output: html_notebook
---

# Packages and Inputs

```{r libraries in use}
library(xgboost) # for xgboost
library(tidyverse) # general utility functions
```

```{r read in our data & put it in a data frame}
diseaseInfo <- read_csv("C:/Users/User/Desktop/university/machine learning/machine learning - salini/dataset/Outbreak_240817.csv")
```

# Preparing our data & selecting features

The core xgboost function requires data to be a matrix.
A matrix is like a dataframe that only has numbers in it. A sparse matrix is a matrix that has a lot zeros in it. XGBoost has a built-in datatype, DMatrix, that is particularly good at storing and accessing sparse matrices efficiently.

```{r print the first few rows of our dataframe}
head(diseaseInfo)
```

our data will need some cleaning before it's ready to be put in a matrix. To prepare our data, we have a number of steps we need to complete:

- Remove information about the target variable from the training data
- Reduce the amount of redundant information
- Convert categorical information (like country) to a numeric format
- Split dataset into testing and training subsets
- Convert the cleaned dataframe to a Dmatrix

## Remove information about the target variable from the training data

```{r remove the columns that have information on our target variable}
diseaseInfo_humansRemoved <- diseaseInfo %>% select(-starts_with("human")) # get the subset of the dataframe that doesn't have labels about humans affected by the disease
```

Let's create a new vector with the labels

```{r get a boolean vector of training labels}
diseaseLabels <- diseaseInfo %>% 
  select(humansAffected) %>% # get the column with the # of humans affected
  is.na() %>% # is it NA?
  magrittr::not() # switch TRUE and FALSE (using function from the magrittr package)

# check out the first few lines
head(diseaseLabels) # of our target variable
head(diseaseInfo$humansAffected) # of the original column
```

## Reduce the amount of redundant information

```{r select just the numeric columns}
diseaseInfo_numeric <- diseaseInfo_humansRemoved %>%
    select(-Id) %>% # the case id shouldn't contain useful information
    select(-c(longitude, latitude)) %>% # location data is also in country data
    select_if(is.numeric) # select remaining numeric columns

# make sure that our dataframe is all numeric
str(diseaseInfo_numeric)
```

## Convert categorical information (like country) to a numeric format

```{r check out the first few rows of the country column}
head(diseaseInfo$country)
```

```{r convert these categories to a matrix}
model.matrix(~country-1,head(diseaseInfo)) # one-hot matrix for just the first few rows of the "country" column
```

```{r convert categorical factor into one-hot encoding}
region <- model.matrix(~country-1,diseaseInfo)

# check out the first few lines of the species
head(diseaseInfo$speciesDescription)
```

```{r add a boolean column to our numeric dataframe indicating whether a species is domestic}

diseaseInfo_numeric$is_domestic <- str_detect(diseaseInfo$speciesDescription, "domestic")
```

```{r create a one-hot matrix of different species}
# grab the last word of each row and use that to create a one-hot matrix of different species

# get a list of all the species by getting the last
speciesList <- diseaseInfo$speciesDescription %>%
    str_replace("[[:punct:]]", "") %>% # remove punctuation (some rows have parentheses)
    str_extract("[a-z]*$") # extract the least word in each row

# convert our list into a dataframe...
speciesList <- tibble(species = speciesList)

# and convert to a matrix using 1 hot encoding
options(na.action='na.pass') # don't drop NA values!
species <- model.matrix(~species-1,speciesList)

# add our one-hot encoded variable and convert the dataframe into a matrix
diseaseInfo_numeric <- cbind(diseaseInfo_numeric, region, species)
diseaseInfo_matrix <- data.matrix(diseaseInfo_numeric)
```

## Split the dataset to model

```{r Split dataset into testing and training subsets}
# get the numb 70/30 training test split
numberOfTrainingSamples <- round(length(diseaseLabels) * .7)

# training data
train_data <- diseaseInfo_matrix[1:numberOfTrainingSamples,]
train_labels <- diseaseLabels[1:numberOfTrainingSamples]

# testing data
test_data <- diseaseInfo_matrix[-(1:numberOfTrainingSamples),]
test_labels <- diseaseLabels[-(1:numberOfTrainingSamples)]
```

```{r Convert the cleaned dataframe to a dmatrix}
# put our testing & training data into two seperates Dmatrixs objects
dtrain <- xgb.DMatrix(data = train_data, label= train_labels)
dtest <- xgb.DMatrix(data = test_data, label= test_labels)
```

# Analysis

## Supervised Learning

```{r set a random seed & shuffle data frame}
set.seed(1234)
diseaseInfo <- diseaseInfo[sample(1:nrow(diseaseInfo)), ]
```

```{r train a model using our training data}
model <- xgboost(data = dtrain,  
                 nround = 2, # max number of boosting iterations
                 objective = "binary:logistic")  # objective function
```

```{r make prediction}
# generate predictions for our held-out testing data
pred <- predict(model, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
```

## Tuning  our Model

```{r}
# train an xgboost model
model_tuned <- xgboost(data = dtrain,          
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 2, # max number of boosting iterations
                 objective = "binary:logistic") # objective function 

# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
```

There are two things we can try to see if we improve our model performance:
- Account for the fact that we have imbalanced classes
- Train for more rounds

```{r re-training our model}
# get the number of negative & positive cases in our data
negative_cases <- sum(train_labels == FALSE)
postive_cases <- sum(train_labels == TRUE)

# train a model using our training data
model_tuned <- xgboost(data = dtrain,           
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 10, # number of boosting rounds
                 early_stopping_rounds = 3, # if we don't see an improvement in this many rounds, stop
                 objective = "binary:logistic", # objective function
                 scale_pos_weight = negative_cases/postive_cases) # control for imbalanced classes

# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
```

... TODO

```{r }
# train a model using our training data
model_tuned <- xgboost(data = dtrain,            
                 max.depth = 3, # maximum depth of each decision tree
                 nround = 10, # number of boosting rounds
                 early_stopping_rounds = 3, # if we don't see an improvement in this many rounds, stop
                 objective = "binary:logistic", # objective function
                 scale_pos_weight = negative_cases/postive_cases, # control for imbalanced classes
                 gamma = 1) # add a regularization term

# generate predictions for our held-out testing data
pred <- predict(model_tuned, dtest)

# get & print the classification error
err <- mean(as.numeric(pred > 0.5) != test_labels)
print(paste("test-error=", err))
```

## Interpretation

```{r }
# plot them features! what's contributing most to our model?
xgb.plot.multi.trees(feature_names = names(diseaseInfo_matrix), 
                     model = model)
```

Because we're using a logistic model here, it's telling us the log-odds rather than the probability

```{r}
# convert log odds to probability
odds_to_probs <- function(odds){
    return(exp(odds) / (1 + exp(odds)))
}

# probability of leaf above countryPortugul
odds_to_probs(-0.599)
```

```{r plotting the importance matrix}
# get information on how important each feature is
importance_matrix <- xgb.importance(names(diseaseInfo_matrix), model = model)

# and plot it!
xgb.plot.importance(importance_matrix)

```

## Unsupervised Learning

```{r}
# diseaseInfo_numeric.pca <- prcomp(diseaseInfo_numeric[, c(1:7,10,11)],
#                                   center = TRUE,
#                                   scale = TRUE)
diseaseInfo_numeric
```

